Questions
- How do species differ in their drought response to variable intensity and their recovery patterns?
- If species differ, do they also vary regionally? For which species?
- Are drought response and recovery mediated by competition and tree size and is this a species specific phenomenon or does it also vary regionally?
Methods
I collected tree ring data from 4 regions across California and performed analyses on detrended growth during drought years where water availability (SPEI) was in the bottom 10th percentile. All tree ring series were spline detrended.
Key responses
\[
Growth Reduction = \frac{\overline{RWI}_{non-drought} - RWI_{drought}}{\overline{RWI}_{non-drought}}
\] \[
Recovery = RWI_{actual} - RWI_{pred}
\]
Where \(RWI_{pred}\) is the predicted growth for a tree given the post-drought year conditions based on hierarchical Bayesian models of all growth years.


Full model approach to Q3
This approach differs in that here we explore the results of the full expression of the model to answer the above questions i.e. the most complex justifiable model. Each species is modeled independently. This approach is a way to avoid the model selection issues we discussed regarding the complexity of question 3.
\[
Reduction_i \sim Normal(\mu_i, \sigma_i)
\]
\[
\mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}SPEI_i + \beta_{2}DBH_i + \beta_{3}BA_i + \beta_{4}SPEI_i\times DBH_i + \beta_{5}SPEI_i \times BA_i
\]
and for recovery:
\[
Recovery_i \sim Normal(\mu_i, \sigma_i)
\]
\[
\mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}Reduction_i + \beta_{2}DBH_i + \beta_{3}BA_i + \beta_{4}Reduction_i\times DBH_i + \beta_{5}Reduction_i \times BA_i
\]
Regionally varying responses to drought intensity or severity could reflect local adaptation.
Descriptions of interaction terms
\(SPEI \times DBH\) smaller or larger trees experience the same drought intensity differently. Perhaps this is due to differences in evaporative demand, root:shoot allocation patterns, height water relationship
\(Reduction \times DBH\) smaller or larger trees recover from equally damaging droughts differently. Potentially due to access to resources, allocation again.
\(SPEI \times BA\) sparse or dense neighborhoods modify the effect of drought intensity. This could be via resource (water) competition. Although because we lack good characterization of the between neighborhood microsite differences density could reflect suitability more than competition.
\(Reduction \times BA\) sparse or dense neighborhoods modify the recovery of trees from equally damaging droughts. This could also be via resource competition although more than just water. Again, patterns may reflect uncharacterized microsite differences rather than competition.
Details
All models converged Rhat ~1 and each model had few divergent samples. Param estimates and plots were prepared with tidybayes. Marginal effects plots were produced with add_fitted_draws() .
Results
Q1 Species differences
Growth Reduction
Table SX. Growth reduction WAIC table
|
|
waic_diff
|
se
|
|
SPEI only
|
0.00000
|
0.000000
|
|
Species + SPEI
|
2.04252
|
3.076878
|
|
Species * SPEI
|
4.74648
|
3.720620
|
Table SX. Growth reduction variance contrasts
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
PJ - AC > 0
|
0.0666103
|
0.0096405
|
0.0505275
|
0.0820601
|
Inf
|
1.0000
|
|
|
PL - AC > 0
|
0.0342796
|
0.0118112
|
0.0155830
|
0.0540833
|
9.9900e+02
|
0.9990
|
|
|
PL - PJ > 0
|
-0.1272120
|
0.0475280
|
-0.2065795
|
-0.0489364
|
5.5304e-03
|
0.0055
|
|
Table SX. Growth reduction intercept contrasts
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
PJ - AC > 0
|
0.0205816
|
0.0136596
|
-0.0024442
|
0.0429330
|
14.094340
|
0.93375
|
|
|
PL - AC > 0
|
0.0103469
|
0.0157787
|
-0.0155560
|
0.0364456
|
2.906250
|
0.74400
|
|
|
PL - PJ > 0
|
-0.0102347
|
0.0161652
|
-0.0368797
|
0.0164271
|
0.356392
|
0.26275
|
|
Recovery
Table SX. Recovery WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.000000
|
0.00000
|
|
Varying intercept
|
4.186948
|
10.25373
|
|
No species effect
|
12.834264
|
12.04065
|
Table SX. Recovery variance contrasts
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
PJ - AC > 0
|
0.0551883
|
0.0086157
|
0.0409969
|
0.0693746
|
Inf
|
1.00000
|
|
|
PL - AC > 0
|
0.0358049
|
0.0107017
|
0.0183191
|
0.0538784
|
3.99900e+03
|
0.99975
|
|
|
PL - PJ > 0
|
-0.0891320
|
0.0502752
|
-0.1715589
|
-0.0051960
|
4.32968e-02
|
0.04150
|
|
Table SX. Recovery intercept contrasts
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
PJ - AC > 0
|
0.0315932
|
0.0175444
|
0.0029861
|
0.0603802
|
27.98551
|
0.96550
|
|
|
PL - AC > 0
|
0.0967908
|
0.0224670
|
0.0598268
|
0.1338717
|
Inf
|
1.00000
|
|
|
PL - PJ > 0
|
0.0651976
|
0.0225358
|
0.0287279
|
0.1016507
|
1332.33333
|
0.99925
|
|
Table SX. Recovery slope contrasts
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
PJ - AC > 0
|
-0.0809188
|
0.0411304
|
-0.1481597
|
-0.0133473
|
0.025641
|
0.02500
|
|
|
PL - AC > 0
|
0.0800334
|
0.0534826
|
-0.0074203
|
0.1685892
|
14.094340
|
0.93375
|
|
|
PL - PJ > 0
|
0.1609522
|
0.0511764
|
0.0771802
|
0.2447245
|
1332.333333
|
0.99925
|
|
Param Plots

Main Figure

Q2 Regional Differences
Growth Reduction
Table SX. A. concolor growth reduction WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.00000
|
0.00000
|
|
No regional effects
|
43.30953
|
12.80732
|
|
Varying intercept
|
45.11601
|
12.72891
|
Table SX. P. jeffreyi growth reduction WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.00000
|
0.00000
|
|
Varying intercept
|
41.83552
|
12.88420
|
|
No regional effects
|
43.82051
|
13.91644
|
Table SX. P. lambertiana growth reduction WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.00000
|
0.000000
|
|
No regional effects
|
18.41681
|
7.836080
|
|
Varying intercept
|
19.29546
|
7.449942
|
Table SX. ICC for regionally varying parameters (AC, growth reduction)
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
region intercept/total
|
0.5970135
|
0.1336668
|
0.3013006
|
0.8868626
|
NA
|
NA
|
|
|
region slope/total
|
0.2677814
|
0.1137323
|
0.0737678
|
0.5785439
|
NA
|
NA
|
|
Table SX. ICC for regionally varying parameters (PJ, growth reduction)
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
region intercept/total
|
0.5486569
|
0.1608815
|
0.2163339
|
0.8879885
|
NA
|
NA
|
|
|
region slope/total
|
0.2554130
|
0.1337445
|
0.0574560
|
0.6456691
|
NA
|
NA
|
|
Table SX. ICC for regionally varying parameters (PL, growth reduction)
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
region intercept/total
|
0.4047434
|
0.3123458
|
0.0035201
|
0.9735754
|
NA
|
NA
|
|
|
region slope/total
|
0.4766134
|
0.3515581
|
0.0141206
|
0.9946826
|
NA
|
NA
|
|
Recovery
Table SX. A. concolor recovery WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.000000
|
0.000000
|
|
Varying intercept
|
1.851447
|
5.964911
|
|
No regional effects
|
12.912958
|
9.351119
|
Table SX. P. jeffreyi recovery WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.000000
|
0.000000
|
|
Varying intercept
|
7.988191
|
8.352711
|
|
No regional effects
|
22.441717
|
12.987328
|
Table SX. P. lambertiana recovery WAIC table
|
|
waic_diff
|
se
|
|
Varying intercept and slope
|
0.000000
|
0.000000
|
|
Varying intercept
|
4.836886
|
8.154183
|
|
No regional effects
|
36.244175
|
11.872226
|
Table SX. ICC for regionally varying parameters (AC, recovery)
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
region intercept/total
|
0.2333188
|
0.2132561
|
0.0152736
|
0.8137307
|
NA
|
NA
|
|
|
region slope/total
|
0.3221096
|
0.2583555
|
0.0039577
|
0.8943126
|
NA
|
NA
|
|
Table SX. ICC for regionally varying parameters (PJ, recovery)
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
region intercept/total
|
0.1958702
|
0.2089063
|
0.0081197
|
0.8032205
|
NA
|
NA
|
|
|
region slope/total
|
0.3258525
|
0.2541065
|
0.0158146
|
0.9298125
|
NA
|
NA
|
|
Table SX. ICC for regionally varying parameters (PL, recovery)
|
Hypothesis
|
Estimate
|
Est.Error
|
CI.Lower
|
CI.Upper
|
Evid.Ratio
|
Post.Prob
|
Star
|
|
region intercept/total
|
0.2531975
|
0.2850897
|
0.0014873
|
0.9548398
|
NA
|
NA
|
|
|
region slope/total
|
0.5320250
|
0.3267092
|
0.0123234
|
0.9933452
|
NA
|
NA
|
|
Main Figure

Q3
Main Figure

